A Simplified Method for Dynamic Equation of Robot in Generalized Coordinate System

This paper presents a simplified method of dynamic equations in a generalized coordinate system, which decouples the relative motion of the front and back links of the robot joint, and maps generalized angular variables to the same angular datum. Because of the decoupling between absolute angle variables, the complexity of the coefficient matrix of the dynamic equation of the system is reduced, which facilitates the application of the actual series robot system. The simplified process is derived in detail, and the equivalent relation between the generalized relative coordinates and the generalized absolute coordinate dynamics is demonstrated. The relation can be extended to the dynamic equations of different generalized coordinate variables. Aimed at the problem that the quasi-input moment vectors obtained in generalized absolute coordinates cannot be directly used without considering the dynamic coupling of the whole system, the linear relationship between the input moment vectors in absolute and relative coordinates is found. In the end, a simplified example of the Euler-Lagrange dynamic equation for multi-degree-of-freedom manipulator is given. The relationship between the two input torque vectors is simulated by MATLAB and verifies that the input torque can be indirectly calculated by finding the quasi input torque under the absolute coordinates.